Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1

Percentage Accurate: 100.0% → 100.0%

Time: 6.4s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))

C

double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - y) / (z - y)
end function

Java

public static double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

Python

def code(x, y, z):
	return (x - y) / (z - y)

Julia

function code(x, y, z)
	return Float64(Float64(x - y) / Float64(z - y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x - y) / (z - y);
end

Wolfram

code[x_, y_, z_] := N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))

C

double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - y) / (z - y)
end function

Java

public static double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

Python

def code(x, y, z):
	return (x - y) / (z - y)

Julia

function code(x, y, z)
	return Float64(Float64(x - y) / Float64(z - y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x - y) / (z - y);
end

Wolfram

code[x_, y_, z_] := N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))

C

double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - y) / (z - y)
end function

Java

public static double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

Python

def code(x, y, z):
	return (x - y) / (z - y)

Julia

function code(x, y, z)
	return Float64(Float64(x - y) / Float64(z - y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x - y) / (z - y);
end

Wolfram

code[x_, y_, z_] := N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x - y}{z - y} \]

Alternative 2: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{y}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) y)))
   (if (<= y -6.6e+46)
     1.0
     (if (<= y -4.7e-60)
       t_0
       (if (<= y -2.8e-83)
         1.0
         (if (<= y 1.15e-170)
           (/ x z)
           (if (<= y 9.5e-137)
             t_0
             (if (<= y 7e-74)
               (/ x z)
               (if (<= y 3.8e-22)
                 (/ (- y) z)
                 (if (<= y 5.5e+47) (/ x z) 1.0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / y;
	double tmp;
	if (y <= -6.6e+46) {
		tmp = 1.0;
	} else if (y <= -4.7e-60) {
		tmp = t_0;
	} else if (y <= -2.8e-83) {
		tmp = 1.0;
	} else if (y <= 1.15e-170) {
		tmp = x / z;
	} else if (y <= 9.5e-137) {
		tmp = t_0;
	} else if (y <= 7e-74) {
		tmp = x / z;
	} else if (y <= 3.8e-22) {
		tmp = -y / z;
	} else if (y <= 5.5e+47) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x / y
    if (y <= (-6.6d+46)) then
        tmp = 1.0d0
    else if (y <= (-4.7d-60)) then
        tmp = t_0
    else if (y <= (-2.8d-83)) then
        tmp = 1.0d0
    else if (y <= 1.15d-170) then
        tmp = x / z
    else if (y <= 9.5d-137) then
        tmp = t_0
    else if (y <= 7d-74) then
        tmp = x / z
    else if (y <= 3.8d-22) then
        tmp = -y / z
    else if (y <= 5.5d+47) then
        tmp = x / z
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x / y;
	double tmp;
	if (y <= -6.6e+46) {
		tmp = 1.0;
	} else if (y <= -4.7e-60) {
		tmp = t_0;
	} else if (y <= -2.8e-83) {
		tmp = 1.0;
	} else if (y <= 1.15e-170) {
		tmp = x / z;
	} else if (y <= 9.5e-137) {
		tmp = t_0;
	} else if (y <= 7e-74) {
		tmp = x / z;
	} else if (y <= 3.8e-22) {
		tmp = -y / z;
	} else if (y <= 5.5e+47) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / y
	tmp = 0
	if y <= -6.6e+46:
		tmp = 1.0
	elif y <= -4.7e-60:
		tmp = t_0
	elif y <= -2.8e-83:
		tmp = 1.0
	elif y <= 1.15e-170:
		tmp = x / z
	elif y <= 9.5e-137:
		tmp = t_0
	elif y <= 7e-74:
		tmp = x / z
	elif y <= 3.8e-22:
		tmp = -y / z
	elif y <= 5.5e+47:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / y)
	tmp = 0.0
	if (y <= -6.6e+46)
		tmp = 1.0;
	elseif (y <= -4.7e-60)
		tmp = t_0;
	elseif (y <= -2.8e-83)
		tmp = 1.0;
	elseif (y <= 1.15e-170)
		tmp = Float64(x / z);
	elseif (y <= 9.5e-137)
		tmp = t_0;
	elseif (y <= 7e-74)
		tmp = Float64(x / z);
	elseif (y <= 3.8e-22)
		tmp = Float64(Float64(-y) / z);
	elseif (y <= 5.5e+47)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / y;
	tmp = 0.0;
	if (y <= -6.6e+46)
		tmp = 1.0;
	elseif (y <= -4.7e-60)
		tmp = t_0;
	elseif (y <= -2.8e-83)
		tmp = 1.0;
	elseif (y <= 1.15e-170)
		tmp = x / z;
	elseif (y <= 9.5e-137)
		tmp = t_0;
	elseif (y <= 7e-74)
		tmp = x / z;
	elseif (y <= 3.8e-22)
		tmp = -y / z;
	elseif (y <= 5.5e+47)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / y), $MachinePrecision]}, If[LessEqual[y, -6.6e+46], 1.0, If[LessEqual[y, -4.7e-60], t$95$0, If[LessEqual[y, -2.8e-83], 1.0, If[LessEqual[y, 1.15e-170], N[(x / z), $MachinePrecision], If[LessEqual[y, 9.5e-137], t$95$0, If[LessEqual[y, 7e-74], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.8e-22], N[((-y) / z), $MachinePrecision], If[LessEqual[y, 5.5e+47], N[(x / z), $MachinePrecision], 1.0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5999999999999996e46 or -4.7e-60 < y < -2.8000000000000001e-83 or 5.4999999999999998e47 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 99.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 99.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 99.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 99.9%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in y around inf 61.3%

      \[\leadsto \color{blue}{1} \]

   if -6.5999999999999996e46 < y < -4.7e-60 or 1.14999999999999993e-170 < y < 9.5000000000000007e-137

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around inf 75.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y - z}} \]
   5. Step-by-step derivation

      1. neg-mul-1 75.1%

         \[\leadsto \color{blue}{-\frac{x}{y - z}} \]

      2. distribute-neg-frac 75.1%

         \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   6. Simplified 75.1%

      \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   7. Taylor expanded in y around inf 54.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 54.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \]

      2. mul-1-neg 54.5%

         \[\leadsto \frac{\color{blue}{-x}}{y} \]

   9. Simplified 54.5%

      \[\leadsto \color{blue}{\frac{-x}{y}} \]

   if -2.8000000000000001e-83 < y < 1.14999999999999993e-170 or 9.5000000000000007e-137 < y < 7.00000000000000029e-74 or 3.80000000000000023e-22 < y < 5.4999999999999998e47

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in y around 0 71.2%

      \[\leadsto \color{blue}{\frac{x}{z}} \]

   if 7.00000000000000029e-74 < y < 3.80000000000000023e-22

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around 0 73.8%

      \[\leadsto \color{blue}{\frac{y}{y - z}} \]

   5. Taylor expanded in y around 0 74.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{z}} \]

      2. neg-mul-1 74.1%

         \[\leadsto \frac{\color{blue}{-y}}{z} \]

   7. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{-y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-60}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 68.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-111}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-23}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1.5e-111)
     t_0
     (if (<= y 1.15e-170)
       (/ x z)
       (if (<= y 9.5e-137)
         (/ (- x) y)
         (if (<= y 9e-69)
           (/ x z)
           (if (<= y 7.2e-23)
             (/ (- y) z)
             (if (<= y 1.8e-10) (/ x z) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.5e-111) {
		tmp = t_0;
	} else if (y <= 1.15e-170) {
		tmp = x / z;
	} else if (y <= 9.5e-137) {
		tmp = -x / y;
	} else if (y <= 9e-69) {
		tmp = x / z;
	} else if (y <= 7.2e-23) {
		tmp = -y / z;
	} else if (y <= 1.8e-10) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-1.5d-111)) then
        tmp = t_0
    else if (y <= 1.15d-170) then
        tmp = x / z
    else if (y <= 9.5d-137) then
        tmp = -x / y
    else if (y <= 9d-69) then
        tmp = x / z
    else if (y <= 7.2d-23) then
        tmp = -y / z
    else if (y <= 1.8d-10) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.5e-111) {
		tmp = t_0;
	} else if (y <= 1.15e-170) {
		tmp = x / z;
	} else if (y <= 9.5e-137) {
		tmp = -x / y;
	} else if (y <= 9e-69) {
		tmp = x / z;
	} else if (y <= 7.2e-23) {
		tmp = -y / z;
	} else if (y <= 1.8e-10) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -1.5e-111:
		tmp = t_0
	elif y <= 1.15e-170:
		tmp = x / z
	elif y <= 9.5e-137:
		tmp = -x / y
	elif y <= 9e-69:
		tmp = x / z
	elif y <= 7.2e-23:
		tmp = -y / z
	elif y <= 1.8e-10:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -1.5e-111)
		tmp = t_0;
	elseif (y <= 1.15e-170)
		tmp = Float64(x / z);
	elseif (y <= 9.5e-137)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= 9e-69)
		tmp = Float64(x / z);
	elseif (y <= 7.2e-23)
		tmp = Float64(Float64(-y) / z);
	elseif (y <= 1.8e-10)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -1.5e-111)
		tmp = t_0;
	elseif (y <= 1.15e-170)
		tmp = x / z;
	elseif (y <= 9.5e-137)
		tmp = -x / y;
	elseif (y <= 9e-69)
		tmp = x / z;
	elseif (y <= 7.2e-23)
		tmp = -y / z;
	elseif (y <= 1.8e-10)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e-111], t$95$0, If[LessEqual[y, 1.15e-170], N[(x / z), $MachinePrecision], If[LessEqual[y, 9.5e-137], N[((-x) / y), $MachinePrecision], If[LessEqual[y, 9e-69], N[(x / z), $MachinePrecision], If[LessEqual[y, 7.2e-23], N[((-y) / z), $MachinePrecision], If[LessEqual[y, 1.8e-10], N[(x / z), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.50000000000000004e-111 or 1.8e-10 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 99.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 99.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 99.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 99.9%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{\frac{y - x}{y}} \]
   5. Step-by-step derivation

      1. div-sub 71.3%

         \[\leadsto \color{blue}{\frac{y}{y} - \frac{x}{y}} \]

      2. *-inverses 71.3%

         \[\leadsto \color{blue}{1} - \frac{x}{y} \]

   6. Simplified 71.3%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

   if -1.50000000000000004e-111 < y < 1.14999999999999993e-170 or 9.5000000000000007e-137 < y < 9.00000000000000019e-69 or 7.1999999999999996e-23 < y < 1.8e-10

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{\frac{x}{z}} \]

   if 1.14999999999999993e-170 < y < 9.5000000000000007e-137

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y - z}} \]
   5. Step-by-step derivation

      1. neg-mul-1 100.0%

         \[\leadsto \color{blue}{-\frac{x}{y - z}} \]

      2. distribute-neg-frac 100.0%

         \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   7. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \]

      2. mul-1-neg 100.0%

         \[\leadsto \frac{\color{blue}{-x}}{y} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{-x}{y}} \]

   if 9.00000000000000019e-69 < y < 7.1999999999999996e-23

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around 0 73.8%

      \[\leadsto \color{blue}{\frac{y}{y - z}} \]

   5. Taylor expanded in y around 0 74.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{z}} \]

      2. neg-mul-1 74.1%

         \[\leadsto \frac{\color{blue}{-y}}{z} \]

   7. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{-y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-111}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-23}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 4: 59.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{y}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+47}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) y)))
   (if (<= y -5e+47)
     1.0
     (if (<= y -2.1e-59)
       t_0
       (if (<= y -2.7e-83)
         1.0
         (if (<= y 1.15e-170)
           (/ x z)
           (if (<= y 9.5e-137) t_0 (if (<= y 3.6e+47) (/ x z) 1.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / y;
	double tmp;
	if (y <= -5e+47) {
		tmp = 1.0;
	} else if (y <= -2.1e-59) {
		tmp = t_0;
	} else if (y <= -2.7e-83) {
		tmp = 1.0;
	} else if (y <= 1.15e-170) {
		tmp = x / z;
	} else if (y <= 9.5e-137) {
		tmp = t_0;
	} else if (y <= 3.6e+47) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x / y
    if (y <= (-5d+47)) then
        tmp = 1.0d0
    else if (y <= (-2.1d-59)) then
        tmp = t_0
    else if (y <= (-2.7d-83)) then
        tmp = 1.0d0
    else if (y <= 1.15d-170) then
        tmp = x / z
    else if (y <= 9.5d-137) then
        tmp = t_0
    else if (y <= 3.6d+47) then
        tmp = x / z
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x / y;
	double tmp;
	if (y <= -5e+47) {
		tmp = 1.0;
	} else if (y <= -2.1e-59) {
		tmp = t_0;
	} else if (y <= -2.7e-83) {
		tmp = 1.0;
	} else if (y <= 1.15e-170) {
		tmp = x / z;
	} else if (y <= 9.5e-137) {
		tmp = t_0;
	} else if (y <= 3.6e+47) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / y
	tmp = 0
	if y <= -5e+47:
		tmp = 1.0
	elif y <= -2.1e-59:
		tmp = t_0
	elif y <= -2.7e-83:
		tmp = 1.0
	elif y <= 1.15e-170:
		tmp = x / z
	elif y <= 9.5e-137:
		tmp = t_0
	elif y <= 3.6e+47:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / y)
	tmp = 0.0
	if (y <= -5e+47)
		tmp = 1.0;
	elseif (y <= -2.1e-59)
		tmp = t_0;
	elseif (y <= -2.7e-83)
		tmp = 1.0;
	elseif (y <= 1.15e-170)
		tmp = Float64(x / z);
	elseif (y <= 9.5e-137)
		tmp = t_0;
	elseif (y <= 3.6e+47)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / y;
	tmp = 0.0;
	if (y <= -5e+47)
		tmp = 1.0;
	elseif (y <= -2.1e-59)
		tmp = t_0;
	elseif (y <= -2.7e-83)
		tmp = 1.0;
	elseif (y <= 1.15e-170)
		tmp = x / z;
	elseif (y <= 9.5e-137)
		tmp = t_0;
	elseif (y <= 3.6e+47)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / y), $MachinePrecision]}, If[LessEqual[y, -5e+47], 1.0, If[LessEqual[y, -2.1e-59], t$95$0, If[LessEqual[y, -2.7e-83], 1.0, If[LessEqual[y, 1.15e-170], N[(x / z), $MachinePrecision], If[LessEqual[y, 9.5e-137], t$95$0, If[LessEqual[y, 3.6e+47], N[(x / z), $MachinePrecision], 1.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000022e47 or -2.09999999999999997e-59 < y < -2.69999999999999991e-83 or 3.60000000000000008e47 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 99.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 99.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 99.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 99.9%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in y around inf 61.3%

      \[\leadsto \color{blue}{1} \]

   if -5.00000000000000022e47 < y < -2.09999999999999997e-59 or 1.14999999999999993e-170 < y < 9.5000000000000007e-137

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around inf 75.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y - z}} \]
   5. Step-by-step derivation

      1. neg-mul-1 75.1%

         \[\leadsto \color{blue}{-\frac{x}{y - z}} \]

      2. distribute-neg-frac 75.1%

         \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   6. Simplified 75.1%

      \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   7. Taylor expanded in y around inf 54.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 54.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y}} \]

      2. mul-1-neg 54.5%

         \[\leadsto \frac{\color{blue}{-x}}{y} \]

   9. Simplified 54.5%

      \[\leadsto \color{blue}{\frac{-x}{y}} \]

   if -2.69999999999999991e-83 < y < 1.14999999999999993e-170 or 9.5000000000000007e-137 < y < 3.60000000000000008e47

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in y around 0 67.2%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+47}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-137}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+25} \lor \neg \left(y \leq 4.3 \cdot 10^{+44}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e+25) (not (<= y 4.3e+44))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+25) || !(y <= 4.3e+44)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7d+25)) .or. (.not. (y <= 4.3d+44))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+25) || !(y <= 4.3e+44)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e+25) or not (y <= 4.3e+44):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e+25) || !(y <= 4.3e+44))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7e+25) || ~((y <= 4.3e+44)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e+25], N[Not[LessEqual[y, 4.3e+44]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999999e25 or 4.29999999999999982e44 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 99.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 99.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 99.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 99.9%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in z around 0 76.8%

      \[\leadsto \color{blue}{\frac{y - x}{y}} \]
   5. Step-by-step derivation

      1. div-sub 76.8%

         \[\leadsto \color{blue}{\frac{y}{y} - \frac{x}{y}} \]

      2. *-inverses 76.8%

         \[\leadsto \color{blue}{1} - \frac{x}{y} \]

   6. Simplified 76.8%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]

   if -6.99999999999999999e25 < y < 4.29999999999999982e44

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around inf 77.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y - z}} \]
   5. Step-by-step derivation

      1. neg-mul-1 77.0%

         \[\leadsto \color{blue}{-\frac{x}{y - z}} \]

      2. distribute-neg-frac 77.0%

         \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   6. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{-x}{y - z}} \]
   7. Step-by-step derivation

      1. frac-2neg 77.0%

         \[\leadsto \color{blue}{\frac{-\left(-x\right)}{-\left(y - z\right)}} \]

      2. div-inv 76.8%

         \[\leadsto \color{blue}{\left(-\left(-x\right)\right) \cdot \frac{1}{-\left(y - z\right)}} \]

      3. remove-double-neg 76.8%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{-\left(y - z\right)} \]

   8. Applied egg-rr 76.8%

      \[\leadsto \color{blue}{x \cdot \frac{1}{-\left(y - z\right)}} \]

   9. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{\frac{x}{z - y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+25} \lor \neg \left(y \leq 4.3 \cdot 10^{+44}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 6: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+37} \lor \neg \left(z \leq 2 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e+37) (not (<= z 2e-29))) (/ (- x y) z) (- 1.0 (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+37) || !(z <= 2e-29)) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.5d+37)) .or. (.not. (z <= 2d-29))) then
        tmp = (x - y) / z
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+37) || !(z <= 2e-29)) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e+37) or not (z <= 2e-29):
		tmp = (x - y) / z
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e+37) || !(z <= 2e-29))
		tmp = Float64(Float64(x - y) / z);
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e+37) || ~((z <= 2e-29)))
		tmp = (x - y) / z;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e+37], N[Not[LessEqual[z, 2e-29]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999962e37 or 1.99999999999999989e-29 < z

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in z around inf 84.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y - x}{z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 84.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y - x\right)}{z}} \]

      2. neg-mul-1 84.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z} \]

      3. neg-sub0 84.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z} \]

      4. associate--r- 84.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      5. neg-sub0 84.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right)} + x}{z} \]

   6. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{\left(-y\right) + x}{z}} \]

   7. Taylor expanded in y around 0 84.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{z} + \frac{x}{z}} \]
   8. Step-by-step derivation

      1. +-commutative 84.0%

         \[\leadsto \color{blue}{\frac{x}{z} + -1 \cdot \frac{y}{z}} \]

      2. mul-1-neg 84.0%

         \[\leadsto \frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)} \]

      3. sub-neg 84.0%

         \[\leadsto \color{blue}{\frac{x}{z} - \frac{y}{z}} \]

      4. div-sub 84.0%

         \[\leadsto \color{blue}{\frac{x - y}{z}} \]

   9. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{x - y}{z}} \]

   if -4.49999999999999962e37 < z < 1.99999999999999989e-29

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in z around 0 85.9%

      \[\leadsto \color{blue}{\frac{y - x}{y}} \]
   5. Step-by-step derivation

      1. div-sub 85.9%

         \[\leadsto \color{blue}{\frac{y}{y} - \frac{x}{y}} \]

      2. *-inverses 85.9%

         \[\leadsto \color{blue}{1} - \frac{x}{y} \]

   6. Simplified 85.9%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+37} \lor \neg \left(z \leq 2 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 7: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.08e+127)
   (/ y (- y z))
   (if (<= y 4e+43) (/ x (- z y)) (- 1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.08e+127) {
		tmp = y / (y - z);
	} else if (y <= 4e+43) {
		tmp = x / (z - y);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.08d+127)) then
        tmp = y / (y - z)
    else if (y <= 4d+43) then
        tmp = x / (z - y)
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.08e+127) {
		tmp = y / (y - z);
	} else if (y <= 4e+43) {
		tmp = x / (z - y);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.08e+127:
		tmp = y / (y - z)
	elif y <= 4e+43:
		tmp = x / (z - y)
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.08e+127)
		tmp = Float64(y / Float64(y - z));
	elseif (y <= 4e+43)
		tmp = Float64(x / Float64(z - y));
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.08e+127)
		tmp = y / (y - z);
	elseif (y <= 4e+43)
		tmp = x / (z - y);
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.08e+127], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+43], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08000000000000001e127

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around 0 90.9%

      \[\leadsto \color{blue}{\frac{y}{y - z}} \]

   if -1.08000000000000001e127 < y < 4.00000000000000006e43

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in x around inf 74.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y - z}} \]
   5. Step-by-step derivation

      1. neg-mul-1 74.1%

         \[\leadsto \color{blue}{-\frac{x}{y - z}} \]

      2. distribute-neg-frac 74.1%

         \[\leadsto \color{blue}{\frac{-x}{y - z}} \]

   6. Simplified 74.1%

      \[\leadsto \color{blue}{\frac{-x}{y - z}} \]
   7. Step-by-step derivation

      1. frac-2neg 74.1%

         \[\leadsto \color{blue}{\frac{-\left(-x\right)}{-\left(y - z\right)}} \]

      2. div-inv 73.9%

         \[\leadsto \color{blue}{\left(-\left(-x\right)\right) \cdot \frac{1}{-\left(y - z\right)}} \]

      3. remove-double-neg 73.9%

         \[\leadsto \color{blue}{x} \cdot \frac{1}{-\left(y - z\right)} \]

   8. Applied egg-rr 73.9%

      \[\leadsto \color{blue}{x \cdot \frac{1}{-\left(y - z\right)}} \]

   9. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{\frac{x}{z - y}} \]

   if 4.00000000000000006e43 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 99.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 99.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 99.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 99.9%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in z around 0 80.3%

      \[\leadsto \color{blue}{\frac{y - x}{y}} \]
   5. Step-by-step derivation

      1. div-sub 80.4%

         \[\leadsto \color{blue}{\frac{y}{y} - \frac{x}{y}} \]

      2. *-inverses 80.4%

         \[\leadsto \color{blue}{1} - \frac{x}{y} \]

   6. Simplified 80.4%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+127}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 8: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e-35) 1.0 (if (<= y 3.5e+45) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e-35) {
		tmp = 1.0;
	} else if (y <= 3.5e+45) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d-35)) then
        tmp = 1.0d0
    else if (y <= 3.5d+45) then
        tmp = x / z
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e-35) {
		tmp = 1.0;
	} else if (y <= 3.5e+45) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e-35:
		tmp = 1.0
	elif y <= 3.5e+45:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e-35)
		tmp = 1.0;
	elseif (y <= 3.5e+45)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e-35)
		tmp = 1.0;
	elseif (y <= 3.5e+45)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e-35], 1.0, If[LessEqual[y, 3.5e+45], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000006e-35 or 3.50000000000000023e45 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 99.9%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 99.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 99.9%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 99.9%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 99.9%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in y around inf 56.5%

      \[\leadsto \color{blue}{1} \]

   if -8.00000000000000006e-35 < y < 3.50000000000000023e45

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

      2. +-commutative 100.0%

         \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

      5. sub0-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

      6. neg-mul-1 100.0%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

      12. neg-mul-1 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

      13. times-frac 100.0%

          \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

      14. metadata-eval 100.0%

          \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

      15. *-lft-identity 100.0%

          \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

   4. Taylor expanded in y around 0 62.3%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 34.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Step-by-step derivation

   1. sub-neg 100.0%

      \[\leadsto \frac{\color{blue}{x + \left(-y\right)}}{z - y} \]

   2. +-commutative 100.0%

      \[\leadsto \frac{\color{blue}{\left(-y\right) + x}}{z - y} \]

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{z - y} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{z - y} \]

   5. sub0-neg 100.0%

      \[\leadsto \frac{\color{blue}{-\left(y - x\right)}}{z - y} \]

   6. neg-mul-1 100.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(y - x\right)}}{z - y} \]

   7. sub-neg 100.0%

      \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{z + \left(-y\right)}} \]

   8. +-commutative 100.0%

      \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(-y\right) + z}} \]

   9. neg-sub0 100.0%

      \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

   10. associate-+l- 100.0%

       \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

   11. sub0-neg 100.0%

       \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-\left(y - z\right)}} \]

   12. neg-mul-1 100.0%

       \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{-1 \cdot \left(y - z\right)}} \]

   13. times-frac 100.0%

       \[\leadsto \color{blue}{\frac{-1}{-1} \cdot \frac{y - x}{y - z}} \]

   14. metadata-eval 100.0%

       \[\leadsto \color{blue}{1} \cdot \frac{y - x}{y - z} \]

   15. *-lft-identity 100.0%

       \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{y - x}{y - z}} \]

4. Taylor expanded in y around inf 33.1%

   \[\leadsto \color{blue}{1} \]

5. Final simplification 33.1%

   \[\leadsto 1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{z - y} - \frac{y}{z - y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ x (- z y)) (/ y (- z y))))

C

double code(double x, double y, double z) {
	return (x / (z - y)) - (y / (z - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x / (z - y)) - (y / (z - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x / (z - y)) - (y / (z - y));
}

Python

def code(x, y, z):
	return (x / (z - y)) - (y / (z - y))

Julia

function code(x, y, z)
	return Float64(Float64(x / Float64(z - y)) - Float64(y / Float64(z - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x / (z - y)) - (y / (z - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (- (/ x (- z y)) (/ y (- z y)))

  (/ (- x y) (- z y)))